# Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevance

## TL;DR

This paper presents exact and approximate analytical solutions to the Weiss equation of ferromagnetism using generalized Lambert functions, providing practical formulas for magnetization and temperature dependence relevant for experiments.

## Contribution

It introduces new exact solutions based on Lambert functions and develops practical approximate formulas for magnetization in ferromagnetic materials.

## Key findings

- Exact solutions derived using generalized Lambert functions.
- Approximate formulas for temperature and field dependence of magnetization.
- Discussion on experimental applications, especially for Curie temperature determination.

## Abstract

The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical solutions are obtained, giving the temperature dependence of the spontaneous magnetization, and also the dependence of the magnetization on both temperature and external magnetic field. The experimental relevance of these results, mainly for the determination of the Curie temperature, is discussed.